ay^'+by=k

Lösung

a y^{^{'}} + b y = k

y = - \frac{e ^{\frac{- b t - c _{1} b}{a}}}{b} + \frac{k}{b}

Schritte zur Lösung

a y^{'} (t) + b y = k

Solve separable ODE:

y = - \frac{e ^{\frac{- b t - c _{1} b}{a}}}{b} + \frac{k}{b}

y = - \frac{e ^{\frac{- b t - c _{1} b}{a}}}{b} + \frac{k}{b}

\frac{d y}{d x} = - \frac{y}{x}

y^{^{'}} - y = 2, t e^{2 t} y (0) = 1

y d y - 2 x y^{2} d x = 0

t^{2} (1 + y^{2}) + 2 y \frac{d y}{d t} = 0, y (0) = 1

x (y^{2} + 10) d x = y (x^{2} + 20) d y